Abstract

In voting rights cases, judges often infer unobservable individ ual vote choices from election data aggregated at the precinct level. That is, one must solve an ill-posed inverse problem to obtain the critical information used in these cases. The ill-posed nature of the problem means that tradi tional frequentist and Bayesian approaches cannot be employed without first imposing a range of assumptions. In order to mitigate the problems result ing from incorporating potentially inaccurate information in these cases, we propose the use of information theoretic methods as a basis for recovering an estimate of the unobservable individual vote choices. We illustrate the empirical non-parametric likelihood methods with some election data.

Highlights

  • Forty years ago, Congress passed the landmark Voting Rights Act (VRA) in a monumental effort to safeguard and protect the voting rights of all U.S citizens, regardless of race or color

  • We demonstrate an information-theoretic basis for information recovery in problems for ecological inference that has the virtue that it rests on a family of minimum distance criterion functions including empirical likelihood and maximum entropy principles

  • We have presented an information theoretic approach as a framework for reasoning in voting rights cases where the data are in aggregate form and the basic corresponding recovery problem is a pure ill-posed inverse problem

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Summary

Introduction

Congress passed the landmark Voting Rights Act (VRA) in a monumental effort to safeguard and protect the voting rights of all U.S citizens, regardless of race or color. In order to recover estimates of the unobservable quantities of interest, we must use indirect aggregate data This results in an ill-posed pure inverse problem that is commonly known as the ecological inference problem (Goodman, 1953). The problem is ill-posed or underdetermined because there are more unknowns than data points and insufficient information to solve the problem uniquely These considerations suggest that these types of ecological inference problems that define the issues in such areas as Voting Rights cases are not amenable to frequentist and Bayesian estimation and inference procedures without the imposition of strong assumptions. We demonstrate an information-theoretic basis for information recovery in problems for ecological inference that has the virtue that it rests on a family of minimum distance criterion functions including empirical likelihood and maximum entropy principles These methods are especially useful to process and recover information when the only available data are partial and incomplete. We conclude with a discussion of generalizations that are a basis of current research

Statement of the Problem
Modeling voting behavior as an ill-posed pure inverse problem
Information Theoretic Formulation and Solution
The MaxEnt voter response formulation
Empirical Results
Uniform reference weights
Non-uniform reference weights
Discussion
Computational aspects
Full Text
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